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Under the topic, "Use of exponents to ex...

Under the topic, "Use of exponents to express small numbers in standard form", the following facts are stated:
1. The speed of light is 300000000 m/sec.
2. The height of the Mount Everest is 8848 m.
3. The diameter of a wire on a computer chip is 0.000003 m.
4. The size of a plant cell is 0.00001275 m.
The above examples are used to express each stated number in standard form. Use of such examples

A

shows the accuracy aspect of numbers

B

reflects the inter-disciplinary approach

C

is made in class to grab the attention of students more interested in science

D

helps the teacher to identify the bright students

Text Solution

AI Generated Solution

The correct Answer is:
To express the given numbers in standard form, we will convert each number into a format that uses exponents. The standard form (or scientific notation) is typically expressed as \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer. ### Step-by-Step Solution: 1. **Speed of Light: 300,000,000 m/sec** - To convert this to standard form, we can express it as: \[ 300,000,000 = 3.0 \times 10^8 \] - **Hint:** Move the decimal point 8 places to the left to get a number between 1 and 10. 2. **Height of Mount Everest: 8,848 m** - Convert this to standard form: \[ 8,848 = 8.848 \times 10^3 \] - **Hint:** Move the decimal point 3 places to the left to get a number between 1 and 10. 3. **Diameter of a Wire on a Computer Chip: 0.000003 m** - Convert this to standard form: \[ 0.000003 = 3.0 \times 10^{-6} \] - **Hint:** Move the decimal point 6 places to the right to express it as a positive number multiplied by a negative power of ten. 4. **Size of a Plant Cell: 0.00001275 m** - Convert this to standard form: \[ 0.00001275 = 1.275 \times 10^{-5} \] - **Hint:** Move the decimal point 5 places to the right to express it in standard form. ### Summary of Results: - Speed of Light: \( 3.0 \times 10^8 \) m/sec - Height of Mount Everest: \( 8.848 \times 10^3 \) m - Diameter of Wire: \( 3.0 \times 10^{-6} \) m - Size of Plant Cell: \( 1.275 \times 10^{-5} \) m
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